# How to convert magnitudes to bolometric luminosity? [duplicate]

If we know a star's magnitudes from several bands(say u,g,r,i,z,J,H,k) and the star's distance, how to calculate Lbol?

Let's suppose the star has a black body spectrum. Is there any manual about the calculation? It's better to have a lot of technical details.

• Are you looking​ for something more complicated than find a bolometric correction? – Rob Jeffries Apr 16 '17 at 8:07
• @Rob yes, these objects are cool and bright in infrared, but I know their magnitudes from 2MASS and WISE, and even Sloan. Convert magnitudes to flux and fit using a blackbody model is enough? – questionhang Apr 16 '17 at 8:39
• They are certainly not blackbodies. You would need to fit with proper stellar models. – Rob Jeffries Apr 17 '17 at 8:28
• @Rob If we know magnitudes and stellar type, how to calculate Lbol? – questionhang Apr 17 '17 at 9:01
• I have added a reference to a relevant table for cool objects. – Rob Jeffries Apr 20 '17 at 11:56

Quoting from Wikipedia,

The bolometric magnitude Mbol, takes into account electromagnetic radiation at all wavelengths. It includes those unobserved due to instrumental pass-band, the Earth's atmospheric absorption, and extinction by interstellar dust. It is defined based on the luminosity of the stars. In the case of stars with few observations, it must be computed assuming an effective temperature. Classically, the difference in bolometric magnitude is related to the luminosity ratio according to:

$M_{bol,*} - M_{bol,sun} = -2.5log_{10}(\frac{L_*}{L_{sun}})$

In August 2015, the International Astronomical Union passed Resolution B2[7] defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power (watts) and irradiance (W/m2), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales, which when combined with incorrect assumed absolute bolometric magnitudes for the Sun could lead to systematic errors in estimated stellar luminosities (and stellar properties calculated which rely on stellar luminosity, such as radii, ages, and so on).

[leading to the accepted definition of] $M_{bol} = -2.5log_{10}(L_*) + 71.1974...$ , where the constant term is the zero-point luminosity $L_0$ .

Dunno if this helps, other than that you have to determine the spectral luminosity of the star in question.